Question

If f(x) = 3x2 1 and g(x) = 1 – x, what is the value of (f –

Answer 1

If f(x) = 3x² + 1 and g(x) = 1 – x, the value of (f – g)(2) is 14

Further explanation

Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.

There are many types of functions in mathematics such as :

• Linear Function → f(x) = ax + b

• Quadratic Function → f(x) = ax² + bx + c
• Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
• Logarithmic function → f(x) = ln x
• Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...

Recall the formulas related to the function such as :

$( f + g )( x ) = f ( x ) + g ( x )$

$( f - g )( x ) = f ( x ) - g ( x )$

$( f \cdot g )( x ) = f ( x ) \cdot g ( x )$

$\left ( \frac{f}{g} \right )(x) = \frac {f(x)}{g(x)} ~, ~ where ~ g(x) \neq 0$

Let us now tackle the problem!

Given:

$f(x) = 3x^2 + 1$

$g(x) = 1 - x$

Unknown:

$(f - g)(2) = ?$

Solution:

$( f - g )( x ) = f ( x ) - g ( x )$

$( f - g )( x ) = (3x^2 + 1) - (1 - x)$

$( f - g )( x ) = 3x^2 + x$

$( f - g )( 2 ) = 3(2)^2 + 2$

$( f - g )( 2 ) = 12 + 2$

$\large { \boxed {( f - g )( 2 ) = 14 } }$

Learn more

• Inverse of Function : brainly.com/question/9289171
• Rate of Change : brainly.com/question/11919986
• Graph of Function : brainly.com/question/7829758

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic

Answer 2

F(x) = 3x^2 + 1
g(x) = 1 - x
(f - g)(x) = 3x^2 + 1 - (1 - x) = 3x^2 + 1 - 1 + x = 3x^2 + x
(f - g)(2) = 3(2)^2 + 2 = 3(4) + 2 = 12 + 2 = 14.